Math Chapter Wise

EnglishUP PCS (Pre) 1994

Q61.The two spheres 2 2 2 x y z 25 and 2 2 2 x y z 18x 24y 40z 225 0 + + − − − + = + + − − − + = + + − − − + = + + − − − + = touch at some point. the point of contact is–

A9 12 4,, 5 5 5 B9 12,,4 5 5 C9 4,12, 5 5 D12 4 9,, 5 5

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EnglishUP PCS (Pre) 1995

Q62.The centre of the sphere (x 1)(x 3) (y 2)(y 4) (z 3) (z 1) 0 is + + + − − + + + + + − − + + + + + − − + + + + + − − + + + = − + = − + = − + = −

A(1,1, 1) B(1, –1, 1) C(2, –3, 2) D(–2, 3, –2)

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EnglishUP PCS (Pre) 1995

Q63.The cone reciprocal to the cone 2 2 2 ax by cz 0 is–

A2 2 2 x y z 0 a b c B2 2 2 x y z 0 a b c C2 2 2 x y z yz zx xy 0 a b c bc ca ab Dnone of these

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EnglishUP PCS (Pre) 1995

Q64.The equation of the sphere whose centre is (2,–3, 4) and the radius 5 is–

A2 2 2/x y z 4x 6y 8z 4 0 B2 2 2/x y z 4x 6y 8z 4 0 C2 2 2/x y z 4x 6y 8z 4 0 D2 2 2/x y z 4x 6y 8z 4 0

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EnglishUP PCS (Pre) 1996

Q65.The equation of the circular cone, which contains the three co-ordinate axes as generators, is–

Ayz zx xy 0 Byz zx xy 0 Cyz zx xy 0 DNone of the these

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EnglishUP PCS (Pre) 1996

Q66.The vertex of the cone 2 2 2 2x 2y 7z 10yz 10zx 2x 2y 26z 17 0, is–

A(2,2,1) B(2,1,1) C(1,1,1) DNone of these

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EnglishUP PCS (Pre) 1996

Q67.The plane 2x y z 12 + + = + + = + + = + + = touches the 2 2 2 x y z 24 + + = + + = + + = + + = sphere at the point

A(2,2, 2) B(4,2, 2) C(4,2, 2) D(2, 2,2)

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EnglishUP PCS (Pre) 1996

Q68.Two spheres of radii 3 and 4 cut orthogonally. The radius of the common circle is:

A12/5 B3/4 C1 D4/3

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EnglishUP PCS (Pre) 1996

Q69.The value of 'a' for which the plane x + y + z = a 3 touches the sphere x2 + y2 + z2 – 2x – 2y – 2z – 6 = 0 will be:

A3 + 3 B–3 – 3 C3 D3

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EnglishUP PCS (Pre) 1999

Q70.The radius of the sphere x2 + y2 + z2 – 2x – 10y – 2z + 2 = 0

A2 B3 C4 D5

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EnglishUP PCS (Pre) 2000

Q71.If the plane 2x – y + az = 0 cuts the cone yz + zx + xy = 0 in perpendicular lines, then the value of a is:

A0 B1 C2 D3

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EnglishUP PCS (Pre) 2000

Q72.The radius of the circle x2 + y2 + z2 + x + y + z– 4 = 0, x + y + z = 0 is:

A1 B–1 C2 D3

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EnglishUP PCS (Pre) 2000

Q73.The radius of the sphere 4(x2 + y2 + z2) – 16x + 20y – 32z + 5 = 0 is:

A4 B5 C6 D7

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EnglishUP PCS (Pre) 2001

Q74.If the equation αx2 +βy2 +2z2 –2αx–4βy–40 = 0 represents a sphere, its radius is:

A5 B2 30 C2 10 D2 15

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EnglishUP PCS (Pre) 2002

Q75.If the equation x2 –y2 +z2 –4x+2y+6z+λ=0 Represents a cone, then the value of λ is equal to:

A8 B10 C12 D14

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EnglishUP PCS (Pre) 2002

Q76.The pole of the plane 3x+4y+5z = 6 with respect to the sphere x2 +y2 +z2 = 12, is:

A(6, 8, 10) B(3, 4, 5) C(1, 1, 1) D(0, 0, 0)

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EnglishUP PCS (Pre) 2002

Q77.The radius of the circle in which the sphere x2 +y2 +z2 –8x+4y+8z–45 = 0 is cut by the plane x–2y+2z = 3, is:

A1 B9 C2 5 D4 5

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EnglishUP PCS (Pre) 2003

Q78.The angle between the line joining the centers of two spheres and there radical plane is–

A0 B4 C3 D2

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EnglishUP PCS (Pre) 2003

Q79.Which one of the following equations represents a cone not having three mutually perpendicular generators:

A2 2 2/x 2y 3z 0 B2 2 2/x 2y 3z 0 C–2xy yz – 3zx 0 + = Dxy 2yz 3zx 0

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EnglishUP PCS (Pre) 2003

Q80.the radius of the sphere 2 2 2 2x y z 2 x 6y 4 z 1 0 is–

A2 2/4 8 B3 3/2 C5 D3

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